International Journal for Quality research UDK- 378.014.3(497.11)
Short Scientific Paper (1.03)
Golam Kabir
1)M. Ahsan Akhtar Hasin
2)1)Bangladesh University of Science and Technology (BUET), Bangladesh,
gk.raju@yahoo.com
2)Bangladesh University of Science and Technology (BUET), Bangladesh, aahasin@ipe.buet.ac.bd
COMPARATIVE ANALYSIS OF TOPSIS AND
FUZZY TOPSIS FOR THE EVALUATION OF
TRAVEL WEBSITE SERVICE QUALITY
Abstract: The Internet revolution has led to significant changes in the way travel agencies interact with customers. Travel websites provide customers diverse services including travel information and products through the Internet. In practical environments, Internet users face a variety of travel website service quality (TWSQ) that is vague from human beings’ subjective judgments, and most criteria have some degree of interdependent or interactive characteristics. In the face of the strong competition environment, in order to profit by making customers proceed with transactions on the websites, travel websites should pay more attention to improve their service quality. This study discusses the major factors for travel agency websites quality from the viewpoint of users' perception and explores the use of multiple-attribute decision making (MADM) approaches for the evaluation of TWSQ. A comparative analysis of Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and Fuzzy TOPSIS methods are illustrated through a practical application from the websites of five travel agencies. Empirical results showed that the proposed methods are viable approaches in solving the evaluation problem of TWSQ.
Keywords: Fuzzy set theory; MADM; TOPSIS; TWSQ
1.
INTRODUCTION
Internet has had a tremendous impact on
today’s travel and tourism business due to the
rapidly growing online market over the past several years 41 . The Internet has become one of the most important channels for business (Teich et al., 2000; Le, 2005). Consumers used the Internet to find travel options, seek the best possible prices, and book reservations for airline tickets, hotel rooms, car rentals, cruises, and tours (Longhi, 2009; Gratzer et al., 2004). Prior studies have pointed out that online travel booking and associated travel services are one of the most successful B2C e-commerce practices (Burns, 2006). Furthermore, many travel service/product suppliers have grasped these potential advantages by establishing their own websites to help their business grow more rapidly (Pan & Fesenmaier, 2000).
A website offers a business not only a platform to promote products or services but also
survive and thrive on the Internet, and willing to invest in online services, it is critical to understand precisely in advance how online customers will evaluate their full service offer and which service quality dimensions are valued most (Jeong et al., 2003).
Parasuraman et al. (1985, 1988) were the first to introduce a formal service quality model. Service quality is measured along five fundamental quality dimensions: tangibles (appearance of physical facilities, equipment, personnel, and communication materials), reliability (the ability of the firm to perform the promised service dependably and accurately), responsiveness (willingness to help customers and provide prompt service), assurance (knowledge and courtesy of the employees and their ability to convey trust and confidence), and empathy (the caring and individualized attention provided to the customer). Zeithaml et al. (2000) developed 11 SERVQUAL-related dimensions based on focus group research. Zeithaml et al. (2000) suggest measuring user interface quality in three dimensions, namely accessibility, navigation and aesthetics. Santos (2003) indicated that service quality is a key determinant in differentiating service offers and building competitive advantages, since the costs of comparing alternatives are relatively low in online environments. A number of researchers (Chand, 2010) used the five dimensions of SERVQUAL instrument and the characteristics of Internet as a basis for developing the measurement dimensions that affect website service quality, but Rowley (2006) revealed that these studies have shown that some of service quality dimensions were different from the five dimensions described by the original SERVQUAL researchers. To better understand the dimensions that affect the online consumer’s TWSQ in virtual context, this study attempts to derive the instrument dimensions of website service quality through modifying moderately the e-SERVQUAL scale developed by Zeithaml et al. (2002) and considering the travel and tourism contexts from the online customers’ perspectives to suit the travel website context. Parasuraman et al. (2005) developed E-S-QUAL scale that effectively captured the nature of electronic service quality from the perspective of online shopping through a Website. The E-S-QUAL scale measures four dimensions of electronic
service quality, namely Efficiency, System Availability, Fulfillment, and Privacy.
To explore the previous related studies, most of the conventional measurement methods for evaluating website service quality use statistical methods to analyze it. During recent years, different website evaluation approaches have been introduced. These deal, for example, with website usability and design (Palmer, 2002), content (Robbins & Stylianou, 2003), quality (Dominic et al., 2010), user acceptance (Shih, 2004), and user satisfaction (Szymanski & Hise, 2000) being the most common outcomes measured to evaluate websites. From a tactical viewpoint, these approaches were good by assessing user attitude towards the website and could be considered as an external user’s view. From a strategic viewpoint, however, little attention was given to evaluating the consistency between web strategy and web presence, which can be considered as an internal evaluation, from the company’s view point.
A1
C1
x11
C2
x12
C3
x13
.
. .
. .
.
Cn
x1n
A2 x21 x22 x23 . . . x2n
A3 x31 x32 x33 . . . x3n
D = . . . . . . . .
. . . . . . . .
. . . . . . . .
Am xm1 xm2 xm3 . . . xmn
capacity. Wang & Chang (2007) applied fuzzy TOPSIS to help the Air Force Academy in Taiwan choose optimal initial training aircraft in a fuzzy environment. Benitez et al. (2007) presented a fuzzy TOPSIS approach for evaluating dynamically the service quality of three hotels of an important corporation in Gran Canaria Island via surveys. Chen et al. (2006) applied fuzzy TOPSIS approach to deal with the supplier selection problem in supply chain system.
The main purpose of this research is to evaluate the major factors for travel agency websites quality from the viewpoint of users' perception and to develop a systematic multiple-attribute evaluation model including the comparison of both TOPSIS and Fuzzy TOPSIS, to find out the effective travel agency websites. Analytic Hierarchy Process (AHP) is applied to determine the weights of evaluation criteria and TOPSIS and fuzzy TOPSIS methods are utilized to rank the service quality of the travel agency websites. This research looks forward to provide some empirical tactics in order to enhance management performance for the evaluation of website service quality.
The remainder of this paper is organized as follows. The theories for the two MADM methods are discussed in detail sequentially in the next section. Section 3 provides the background information for the case study problem and the justification of the proposed model. The discussion that summarizes the empirical results is given in Section 4. Finally, the last section contains some conclusions reached in this paper.
2.
TOPSIS METHOD AND FUZZY
TOPSIS METHOD
2.1TOPSIS Method
TOPSIS is one of the useful Multi Attribute Decision Making techniques that are very simple and easy to implement, so that it is used when the user prefers a simpler weighting approach. On the other hand, the AHP approach provides a decision hierarchy and requires pairwise comparison among criteria (Lee et al., 2001). TOPSIS method was firstly proposed by Hwang & Yoon (1981). According to this technique, the best alternative would be the one that is nearest to the positive ideal solution and farthest from the negative ideal solution (Benitez et al., 2007). The positive ideal solution is a solution that maximizes the benefit criteria and minimizes the cost criteria, whereas the negative ideal solution maximizes the cost criteria and minimizes the benefit criteria (Wang & Chang, 2007; Wang & Elhag, 2006; Wang & Lee, 2007; Lin et al., 2008). In other words, the positive ideal solution is composed of all best values attainable of criteria, whereas the negative ideal solution consists of all worst values attainable of criteria (Ertuğrul & Karakasoğlu, 2009).
A MADM problem with m alternatives (A1,
A2,…., Am) that are evaluated by n attributes (C1,
C2,…., Cn) can be viewed as a geometric system
with m points in n-dimensional space. An element xij of the matrix indicates the performance rating of the ith alternative, Ai, with respect to the jth
attribute, Cj, as shown in Eqs. (1).
The terms used in the present study are briefly defined as follows:
Attributes: Attributes (Cj, j = 1, 2,…., n) should
provide a means of evaluating the levels of an objective. Each alternative can be characterized by a number of attributes.
i
Alternatives: These are synonymous with
‘options’ or ‘candidates’. Alternatives (Ai, i = 1,2,
….,m) are mutually exclusive of each other. Attribute weights: Weight values (wj) represent the
relative importance of each attribute to the others. W = {wj|j = 1, 2,….,n}.
Normalization: Normalization seeks to obtain comparable scales, which allows attribute comparison. The vector normalization approach divides the rating of each attribute by its norm to calculate the normalized value of xij as defined in
, i = 1,…,m (6)
Similarly, the separation of each alternative from the negative ideal alternative is:
, i = 1,…, m (7)
Step 5: Calculate the relative closeness to the ideal solution or similarities to ideal solution CCi*
C * = S –/ (S * +S –), 0 C * 1 (8)
i i i * i i * –
Eqs. (2): Note that 0 * = 0, ≤when Ci ≤ A =A*1, where Ci = 0 when Ai = A ,
i = 1, 2,….,m; j = 1, 2,….,n and Ci i *
Step 6: By comparing Ci values, the ranking of
alternatives are determined. Choose an alternative *
(2) with maximum Ci or rank alternatives according
Given the above terms, the formal TOPSIS procedure is defined as follows:
Step 1: Construct normalized decision matrix. This step transforms various attribute dimensions into non-dimensional attributes, which allows comparisons across criteria.
Step 2: Construct the weighted normalized decision matrix. Assume a set of weights for each criteria wj for j = 1,…,n. Multiply each column of
the normalized decision matrix by its associated weight. An element of the new matrix is:
vij = wj rij , for i = 1, 2,…, m; j = 1, 2,…,n (3)
Step 3: Determine the positive ideal (A*) and negative ideal (A–) solutions. The A* and A– are defined in terms of the weighted normalized values, as shown in Eqs. (4) and (5), respectively: Positive Ideal solution: * * *
to C * in descending order.
2.2Fuzzy TOPSIS Model
It is often difficult for a decision-maker to assign a precise performance rating to an alternative for the attributes under consideration. The merit of using a fuzzy approach is to assign the relative importance of attributes using fuzzy numbers instead of precise numbers. This section extends the TOPSIS to the fuzzy environment (Yang & Hung, 2007). This method is particularly suitable for solving the group decision-making problem under fuzzy environment. The rationale of fuzzy theory has been reviewed before the development of fuzzy TOPSIS. The mathematics concept borrowed from Ashtiani et al. (2009), Buyukozkan et al. (2007) and Wang & Chang (2007), Kabir et A* = { v1 , …,vn }, where vj ={ max (vij) if j J
; min (vij) if j J' } (4)
Negative ideal solution:
al. (2011); Bahram and Asghari, 2011; Kalpande et al., 2010; Tadic et al., 2010):
Definition 1: A fuzzy set M
– – discourse X is characterized by a membership
A– = { v1 , …,vn }, where v' = { min (vij) if j J ; function µM (x) which associates with each
max (vij) if j J' } (5)
Where J is a set of benefit attributes (larger-the- better type) and J' is a set of cost attributes (smaller-the-better type).
Step 4: Calculate the separation measures for each alternative.
The separation of each alternative from the positive ideal alternative is:
element x in X, a real number in the interval [0, 1]. The function value µM (x) is termed the grade of
membership of x in M
C1 C2 C3 . . .
A1 11 12 13 . . .
A2 21 22 23 . . .
= . . . . . . .
. . . . . . .
. . . . . . .
Am m1 m2 m3 . . .
µ (x\ =
0,
(x-a1)/(b1-a1), (c1-x)/(b1- c1),
0,
x ≤ a1, a1 < x ≤ b1, b1 < x ≤ c1, x > c1,
(9)
Definition 2: Let M 1 = (a1, b1, c1) and 2 = (a2, b2, c2) are two triangular fuzzy numbers, then the vertex method is defined to calculate the distance between them.
d(M 1, M 2) =
(10)
Property 1: Assuming that both M 1 = (a1, b1, c1) and 2 = (a2, b2, c2) are real numbers, then the
distance measurement d (M 1, M 2) is identical
to the Euclidian distance.
Property 2: Assuming that M 1 = (a1, b1, c1) and
2 = (a2, b2, c2) are two TFNs, then their operational laws can be expressed as follows:
1⊕ 2 = a1 + a2, b1 + b2, c1 + c2 (11) 1Θ 2 = a1 −a2, b1 −b2, c1 −c2 (12) 1 ⊗ 2 = a1a2, b1b2, c1c2 (13)
The fuzzy MADM can be concisely expressed in matrix format as Eqs. (14) and (15).
Cn
1n
2n
. . .
mn
[ 1 2 n] (15)
Where ij , i =1, 2,…,m, j = 1, 2,….,n and j ,
j = 1, 2,….,n are linguistic triangular fuzzy numbers, ij = (aij, bij, cij) and j = (wj1,
wj2, wj3). Note that ij is the performance rating of
the ith alternative, Ai, with respect to the jth
attribute,
Cj and wj represents the weight of the jth attribute,
Cj.
The normalized fuzzy decision matrix denoted by R
= [ ij]m×n (16)
The weighted fuzzy normalized decision matrix is shown as Eqs. (17):
Given the above fuzzy theory, the proposed fuzzy TOPSIS procedure is then defined as follows:
(17)
Step 1: Choose the linguistic ratings ( ij , i = 1,
j
j
i i i
The fuzzy linguistic rating ( ij) preserves the
property that the ranges of normalized triangular fuzzy numbers belong to [0, 1]; thus, there is no need for a normalization procedure. For this instance, the defined by Eqs. (15) is equivalent to the defined by Eqs. (17).
Step 2: Construct the weighted normalized fuzzy decision matrix. The weighted normalized value
is calculated by Eqs. (18).
Step 3: Identify positive ideal (A*) and negative ideal (A–) solutions. The fuzzy positive-ideal solution (FPIS, A*) and the fuzzy negative-ideal solution (FNIS, A–) are shown as Eqs. (18) and (19):
Positive Ideal solution:
testing the propositions that were developed. To preserve confidentiality, the five travel websites are referenced as WA1, WA2, WA3, WA4 and WA5.
A consumer survey was conducted towards meeting the objectives of the present study. A structured undisguised questionnaire was developed containing 37 closed questions and 5 open questions. The questionnaire was sent by e- mail to a random and convenience sample of the travel service providers, customers, academic experts and professional executives of about 412 contacts on April 10th 2010, with the invitation to complete the questionnaire for at least one travel website and 253 respondents completed the questionnaire, a response rate of 61.4%.
* * *
1 2 n
*
={( max For the actual survey, individuals from the
ij | i = 1,2,…,m), j = 1,2,…,n}
(18) Negative ideal solution:
sample were invited by e-mail to participate in the Web survey. The e-mail invitation letter described the purpose of the study and assured the
ˉ ˉ ˉ
1 2 n ˉ ={( max confidentiality of information provided by
ij | i = 1,2,…,m), j = 1,2,…,n}
(19)
Step 4: Calculate separation measures. The distance of each alternative from A* and A–can be currently calculated using Eqs. (20) and (21).
i = 1,
2,….,m (20)
i = 1,
2,….,m (21)
Step 5: Calculate similarities to ideal solution. This step solves the similarities to an ideal solution by Eqs. (22):
respondents. The participants were asked to continue the survey only if they have taken services from any travel service providers. Then, the participants were directed to a Web site by clicking on a URL in the e-mail to reach the survey webpage. About a week later, a second reminder e-mail was sent to the people who did not respond to the Web survey. Two weeks after, a third reminder e-mail was sent to the people who did not respond to the Web survey.
The majority of respondents aged between 17- 25 and 43-62, while 39.7% of the respondents were female. The respondents of the study also indicated that they were employed in many
CCi* = d –/ (d *+d –) (22) different occupations. 38.7% of the respondents
Step 6: Rank preference order. Choose an alternative with maximum CCi* or rank
alternatives according to CCi* in descending
order. The proposed fuzzy TOPSIS is then applied to the case study as shown in the next section.
3.AN EMPIRICAL STUDY
A comparison of five existing travel websites in Bangladesh serves to validate the model by
Figure 1: The objective hierarchy for evaluation of travel website service
The main goal of the questionnaire is to identify the factors for travel agency websites quality from the viewpoint of users' perception. The selection of the potential criteria and evaluation of the service website quality is conducted by a committee of experts that are comprised of seven professionals from practice and three from the academia. The committee of experts identifies effective and major criteria among all the attributes shown to the respondents in the survey. The hierarchy structure adopted in this study was developed by the committee of experts as a means of dealing with assessing the service quality of travel website is shown in Figure 1: the objective hierarchy for evaluation of travel website service.
The performance ratings given by the committee of experts for the 17 criteria from 5 attributes with respect to the five alternatives are summarized in Table 1 decision matrix. The decision matrix from Table 1 is used for the TOPSIS analysis and fuzzy TOPSIS analysis.
3.1 Empirical illustrations for TOPSIS method
Table 1: Decision matrix
(WA1) (WA2) (WA3) (WA4) (WA5)
(C11) 8 7 7 6 8
(C12) 6 8 7 5 7
(C13) 8 7 6 6 5
(C21) 7 5 8 7 5
(C22) 8 5 6 7 6
(C23) 4 3 5 5 4
(C31) 5 6 8 8 5
(C32) 7 5 7 7 6
(C33) 4 5 4 5 6
(C34) 6 7 9 6 8
(C41) 6 6 9 5 7
(C42) 8 5 7 6 7
(C43) 7 8 6 5 6
(C44) 9 7 8 7 5
(C51) 8 7 7 8 6
(C52) 9 9 7 6 6
(C53) 6 6 8 7 7
Table 2: Normalized decision matrix for TOPSIS analysis
(WA1) (WA2) (WA3) (WA4) (WA5)
(C11) 0.2777 0.2653 0.2386 0.2304 0.3123
(C12) 0.2083 0.3032 0.2386 0.192 0.2733
(C13) 0.2777 0.2653 0.2045 0.2304 0.1952
(C21) 0.243 0.1895 0.2726 0.2688 0.1952
(C22) 0.2777 0.1895 0.2045 0.2688 0.2343
(C23) 0.1388 0.1137 0.1704 0.192 0.1562
(C31) 0.1736 0.2274 0.2726 0.3072 0.1952
(C32) 0.243 0.1895 0.2386 0.2688 0.2343
(C33) 0.1388 0.1895 0.1363 0.192 0.2343
(C34) 0.2083 0.2653 0.3067 0.2304 0.3123
(WA1) (WA2) (WA3) (WA4) (WA5)
(C41) 0.2083 0.2274 0.3067 0.192 0.2733
(C42) 0.2777 0.1895 0.2386 0.2304 0.2733
(C43) 0.243 0.3032 0.2045 0.192 0.2343
(C44) 0.3124 0.2653 0.2726 0.2688 0.1952
(C51) 0.2777 0.2653 0.2386 0.3072 0.2343
(C52) 0.3124 0.3411 0.2386 0.2304 0.2343
(C53) 0.2083 0.2274 0.2726 0.2688 0.2733
The second step requires the attribute weight information to calculate the weighted normalized ratings. The relative importance of each criterion
Level of importance (aij)
Linguistic definition for comparison of the ith and the jth items
1 The i
th
item is equal important as the jth item
3
The ith item is slightly more important than the jth item
5 The i
th
item is more important than the jth item
7
The ith item is strongly more important than the jth item
9
The ith item is extremely more important than the jth item
2,4,6,8
The intermediate values between two adjacent judgments
1/aij = aji
The inverse comparison between the ith and the jth items
Table 3: Linguistic definition for importance ratios of two selected items
For instance, the judgment matrix and the weights of four criteria under the third attribute i.e., responsiveness, given by the committee of experts can be figured out as Table 4.
The weights of the all evaluation objectives can be obtained in the same manner as shown in Table 5.
Then, weighted normalized matrix is formed by multiplying each value with their corresponding weights. Table 6 shows the normalized weighted decision matrix for each alternative with respect to the each criterion. Positive and negative ideal solutions are determined by taking the maximum and minimum values for each criterion using Eqs. (4) and (5). Then the distance of each alternative from PIS and NIS with respect to each criterion are calculated with the help of Eqs. (6) and (7). Table 6 shows the separation measure of each alternative form PIS and NIS. The closeness coefficient of each logistics service provider is calculated by using Eqs. (8) and the ranking of the alternatives are determined according to these values in Table 6.
Table 4: The pairwise comparison table of the relative importance
Criteria of Attribute (Reliability) C31 C32 C33 C34 Weights
Proper website function (C31) 1 5 3 7 0.56
Privacy security policy (C32) 1/5 1 1/3 3 0.12
Uncommon occurrence of website crash (C33) 1/3 3 1 5 0.26
Provide accurate information (C34) 1/7 1/3 1/5 1 0.06
Table 5: The weight of all evaluation objectives
Criteria Attributes Weight Criteria Attributes Weight
(C1) 0.23 (C33) 0.26
(C11) 0.43 (C34) 0.06
(C12) 0.38 (C4) 0.18
(C13) 0.19 (C41) 0.33
(C2) 0.12 (C42) 0.19
(C21) 0.51 (C43) 0.39
(C22) 0.30 (C44) 0.09
(C23) 0.19 (C5) 0.11
(C3) 0.36 (C51) 0.28
(C31) 0.56 (C52) 0.61
Finally, the sixth step ranks the alternatives according to Table 6. The order of ranking the alternatives using TOPSIS method results as follows:
WA2 > WA3 > WA4 > WA1 > WA5
According to the final scores, it can be concluded that the website quality of WA2 provides the best
information and service from the viewpoint of users' perception.
Table 6: TOPSIS analysis results
(WA1) (WA2) (WA3) (WA4) (WA5) vj* vjˉ
(C11) 0.1194 0.1141 0.1026 0.0991 0.1343 0.1343 0.0991
(C12) 0.0792 0.1152 0.0907 0.073 0.1039 0.1152 0.073
(C13) 0.0528 0.0504 0.0389 0.0438 0.0371 0.0528 0.0371
(C21) 0.1239 0.0966 0.139 0.1371 0.0996 0.139 0.0966
(C22) 0.0833 0.0569 0.0614 0.0806 0.0703 0.0833 0.0569
(C23) 0.0264 0.0216 0.0324 0.0365 0.0297 0.0216 0.0365
(C31) 0.0972 0.1273 0.1527 0.172 0.1093 0.172 0.0972
(C32) 0.0292 0.0227 0.0286 0.0323 0.0281 0.0323 0.0227
(C33) 0.0361 0.0493 0.0354 0.0499 0.0609 0.0354 0.0609
(C34) 0.0125 0.0159 0.0184 0.0138 0.0187 0.0187 0.0125
(C41) 0.0687 0.075 0.1012 0.0634 0.0902 0.1012 0.0634
(C42) 0.0528 0.036 0.0453 0.0438 0.0519 0.0528 0.036
(C43) 0.0948 0.1182 0.0798 0.0749 0.0914 0.1182 0.0749
(C44) 0.0281 0.0239 0.0245 0.0242 0.0176 0.0281 0.0176
(C51) 0.0778 0.0743 0.0668 0.086 0.0656 0.086 0.0656
(C52) 0.1906 0.2081 0.1455 0.1405 0.1429 0.2081 0.1405
(C53) 0.0229 0.025 0.03 0.0296 0.0301 0.0301 0.0229
Si* 0.09717 0.07968 0.09280 0.10742 0.11126
Siˉ 0.07599 0.09959 0.08447 0.09159 0.06410
Ci* 0.43884 0.55553 0.4765 0.46023 0.36553
3.2 Empirical illustrations for Fuzzy
TOPSIS method
Numeric performance ratings of Table 1 are adopted again for the Fuzzy TOPSIS analysis. In order to transform the performance ratings to fuzzy linguistic variables as discussed in the previous section, the performance ratings in Table 1 are normalized into the range of [0,1] by Eqs. (23) and (24) (Cheng, 1999):
(i)The larger the better type:
rij = [xij - min{xij}] / [max{xij} – min{xij}] (23)
(ii)The smaller the better type:
rij = [max{xij}- xij] / [max{xij} – min{xij}] (24)
For the present study, C23 and C33 are the smaller- the better type, the others belong to the larger-the- better type. Table 7 shows the Normalized decision matrix for fuzzy TOPSIS analysis transformed from Table 1.
3.2.1 Fuzzy membership function
Among the commonly used fuzzy numbers, triangular and trapezoidal fuzzy numbers are likely to be the most adoptive ones due to their simplicity in modeling and easy of interpretation. Both triangular and trapezoidal fuzzy numbers are applicable to the present study. As triangular fuzzy number can adequately represent the seven-level fuzzy linguistic variables and thus, is used for the analysis hereafter. A transformation table can be found as shown in Table 8. For example, the fuzzy variable - Very Low has its associated triangular fuzzy number with minimum of 0.00, mode of 0 and maximum of 0.1. The same definition is then
applied to the other fuzzy variables Low, Medium Low, Medium, Medium High, High and Very High. Figure 2 illustrates the fuzzy membership functions.
The next step uses the fuzzy membership function to transform Table 7 into Table 9 as explained by the following example. If the numeric rating is 0.67, then its fuzzy linguistic variable is ‘‘MH’’. This transformation is also applied to the attributes respectively. Then, the resulting fuzzy linguistic variables are show as Table 9.
Table 7: Normalized decision matrix for fuzzy TOPSIS analysis
(WA1) (WA2) (WA3) (WA4) (WA5)
(C11) 1 0.5 0.5 0 1
(C12) 0.33 1 0.67 0 0.67
(C13) 1 0.67 0.33 0.33 0
(C21) 0.67 0 1 0.67 0
(C22) 1 0 0.33 0.67 0.33
(C23) 0.5 1 0 0 0.5
(C31) 0 0.33 1 1 0
(C32) 1 0 1 1 0.5
(C33) 1 0.5 1 0.5 0
(C34) 0 0.33 1 0 0.67
(C41) 0.25 0.25 1 0 0.5
(C42) 1 0 0.67 0.33 0.67
(C43) 0.67 1 0.33 0 0.33
(C44) 1 0.5 0.75 0.5 0
(C51) 1 0.5 0.5 1 0
(C52) 1 1 0.33 0 0
(C53) 0 0 1 0.5 0.5
Table 8: Linguistic variable and the fuzzy triangular membership functions
Linguistic variable Triangular fuzzy number
Very Low (VL) 0,0,0.1
Low (L) 0,0.1,0.30
Medium Low (ML) 0.1,0.3,0.5
Medium (M) 0.3,0.5,0.7
Medium High (MH) 0.5,0.7,0.9
High (H) 0.7,0.9,1
(WA1) (WA2) (WA3) (WA4) (WA5)
(C11) VH M M VL VH
(C12) ML VH MH VL MH
(C13) VH MH ML ML VL
(C21) MH VL VH MH VL
(C22) VH VL ML MH ML
(C23) M VH VL VL M
(C31) VL ML VH VH VL
(C32) VH VL VH VH M
(C33) VH M VH M VL
(C34) VL ML VH VL MH
(C41) ML ML VH VL M
(C42) VH VL MH ML MH
(C43) MH VH ML VL ML
(C44) VH M MH M VL
(C51) VH M M VH VL
(C52) VH VH ML VL VL
(C53) VL VL VH M M
Figure 2: Fuzzy triangular membership functions
Table 9: Decision matrix using fuzzy linguistic variables
The fuzzy linguistic variable is then transformed into a fuzzy triangular membership function as shown in Table 10. This is the first step of the fuzzy TOPSIS analysis. The fuzzy attribute weight is also collected in Table 10.
The second step in the analysis is to find the weighted fuzzy decision matrix. Using Eqs. (17) and the fuzzy multiplication Eqs. (13), the resulting fuzzy weighted decision matrix is shown as Table 11.
For the fourth step, the distance of each alternative from A* and A– can be currently calculated using Eqs. (20) and (21). The fifth step solves the similarities to an ideal solution by Eqs. (22). The resulting fuzzy TOPSIS analyses are summarized in Table 12.
Based on the Table 12, the order of ranking the alternatives using fuzzy TOPSIS method results as follows:
WA2 > WA1 > WA3 > WA4 > WA5
In this section, the existing precise values have been transformed to fuzzy linguistic variables in order to illustrate the concept of the proposed fuzzy-based method. Based on the fuzzy TOPSIS analysis, a conclusion can be drawn from the viewpoint of users' perception that the website quality of WA2 provides the best information and
Table 10: Fuzzy decision matrix and fuzzy attribute weights
(WA1) (WA2) (WA3) (WA4) (WA5) Weight
(C11) 0.9,1,1 0.3,0.5,0.7 0.3,0.5,0.7 0,0,0.1 0.9,1,1 0.3,0.5,0.7
(C12) 0.1,0.3,0.5 0.9,1,1 0.5,0.7,0.9 0,0,0.1 0.5,0.7,0.9 0.1,0.3,0.5
(C13) 0.9,1,1 0.5,0.7,0.9 0.1,0.3,0.5 0.1,0.3,0.5 0,0,0.1 0,0.1,0.3
(C21) 0.5,0.7,0.9 0,0,0.1 0.9,1,1 0.5,0.7,0.9 0,0,0.1 0.3,0.5,0.7
(C22) 0.9,1,1 0,0,0.1 0.1,0.3,0.5 0.5,0.7,0.9 0.1,0.3,0.5 0.1,0.3,0.5
(C23) 0.3,0.5,0.7 0.9,1,1 0,0,0.1 0,0,0.1 0.3,0.5,0.7 0,0.1,0.3
(C31) 0,0,0.1 0.1,0.3,0.5 0.9,1,1 0.9,1,1 0.0,0.1 0.3,0.5,0.7
(C32) 0.9,1,1 0,0,0.1 0.9,1,1 0.9,1,1 0.3,0.5,0.7 0,0.1,0.3
(C33) 0.9,1,1 0.3,0.5,0.7 0.9,1,1 0.3,0.5,0.7 0,0,0.1 0.1,0.3,0.5
(C34) 0,0,0.1 0.1,0.3,0.5 0.9,1,1 0,0,0.1 0.5,0.7,0.9 0,0.1,0.3
(C41) 0.1,0.3,0.5 0.1,0.3,0.5 0.9,1,1 0,0,0.1 0.3,0.5,0.7 0.1,0.3,0.5
(C42) 0.9,1,1 0,0,0.1 0.5,0.7,0.9 0.1,0.3,0.5 0.5,0.7,0.9 0,0.1,0.3
(C43) 0.5,0.7,0.9 0.9,1,1 0.1,0.3,0.5 0,0,0.1 0.1,0.3,0.5 0.1,0.3,0.5
(C44) 0.9,1,1 0.3,0.5,0.7 0.5,0.7,0.9 0.3,0.5,0.7 0,0,0.1 0,0.1,0.3
(C51) 0.9,1,1 0.3,0.5,0.7 0.3,0.5,0.7 0.9,1,1 0,0,0.1 0.1,0.3,0.5
(C52) 0.9,1,1 0.9,1,1 0.1,0.3,0.5 0,0,0.1 0,0,0.1 0.5,0.7,0.9
(C53) 0.0,0.1 0,0,0.1 0.9,1,1 0.3,0.5,0.7 0.3,0.5,0.7 0,0.1,0.3
Table 11 shows that, the elements ij are the fuzzy negative-ideal solution (FNIS, * – A–) can
normalized positive triangular fuzzy numbers and their ranges belong to the closed interval [0, 1]. Thus, fuzzy positive-ideal solution (FPIS, A*) and
be defined as: j = (1, 1, 1) and j = (0, 0, 0), j
= 1, 2,…., n. This is the third step of the fuzzy
TOPSIS analysis.
Table 11: Fuzzy-weighted decision matrix
(WA1) (WA2) (WA3) (WA4) (WA5)
(C11) 0.27,0.5,0.7 0.09,0.25,0.49 0.09,0.25,0.49 0,0,0.07 0.27,0.5,0.7
(C12) 0.01,0.09,0.25 0.09,0.3,0.5 0.05,0.21,0.45 0,0,0.05 0.05,0.21,0.45
(C13) 0,0.1,0.3 0,0.07,0.27 0,0.03,0.15 0,0.03,0.15 0,0,0.03
(C21) 0.15,0.35,0.63 0,0,0.07 0.27,0.5,0.7 0.15,0.35,0.63 0,0,0.07
(C22) 0.09,0.3,0.5 0,0,0.05 0.01,0.09,0.25 0.05,0.21,0.45 0.01,0.09,0.25
(C23) 0,0.05,0.21 0,0.1,0.3 0,0,0.03 0,0,0.03 0,0.05,0.21
(C31) 0,0,0.07 0.03,0.15,0.35 0.27,0.5,0.7 0.27,0.5,0.7 0,0,0.07
(C32) 0,0.1,0.3 0,0,0.03 0,0.1,0.3 0,0.1,0.3 0,0.05,0.21
(C33) 0.09,0.3,0.5 0.03,0.15,0.35 0.09,0.3,0.5 0.03,0.15,0.35 0,0,0.05
(C34) 0,0,0.03 0,0.03,0.15 0,0.1,0.3 0,0,0.03 0,0.07,0.27
(C41) 0.01,0.09,0.25 0.01,0.09,0.25 0.09,0.3,0.5 0,0,0.05 0.03,0.15,0.35
(C42) 0,0.1,0.3 0,0,0.03 0,0.07,0.27 0,0.03,0.15 0,0.07,0.27
(C43) 0.05,0.21,0.45 0.09,0.3,0.5 0.01,0.09,0.25 0,0,0.05 0.01,0.09,0.25
(C44) 0,0.1,0.3 0,0.05,0.21 0,0.07,0.27 0,0.05,0.21 0,0,0.03
(C51) 0.09,0.3,0.5 0.03,0.15,0.35 0.03,0.15,0.35 0.09,0.3,0.5 0,0,0.05
(C52) 0.45,0.7,0.9 0.45,0.7,0.9 0.05,0.21,0.45 0,0,0.09 0,0,0.09
4.
DISCUSSIONS
According to the TOPSIS and fuzzy TOPSIS methods, the preference order of the alternatives is summarized in Table 13. It is evident that both methods lead to the choice of WA2; hence, travel
website of WA2 shows the highest service quality.
Other than WA2, the preferences vary between
methods. The fuzzy TOPSIS concludes with the order of ranking WA2 > WA1 > WA3 > WA4 >
WA5, whereas TOPSIS method concludes with the
order of ranking WA2 > WA3 > WA4 > WA1 >
WA5. Due to the MADM nature of the proposed
problem, an optimal solution may not exist; however, the systematic evaluation of the MADM problem can reduce the risk of a poor service quality selection.
When precise performance ratings are available, the TOPSIS method is considered to be a viable approach in solving a TWSQ problem. Fuzzy TOPSIS is a preferred choice for the instance of imprecise or vague performance ratings in solving the proposed service quality problem.
Table 12: Fuzzy TOPSIS analysis
j1 j2 j3 j4 j5 A* Aˉ
(C11) 0.27,0.5,0.7 0.09,0.25,0.49 0.09,0.25,0.49 0,0,0.07 0.27,0.5,0.7 1,1,1 0,0,0
(C12) 0.01,0.09,0.25 0.09,0.3,0.5 0.05,0.21,0.45 0,0,0.05 0.05,0.21,0.45 1,1,1 0,0,0
(C13) 0,0.1,0.3 0,0.07,0.27 0,0.03,0.15 0,0.03,0.15 0,0,0.03 1,1,1 0,0,0
(C21) 0.15,0.35,0.63 0,0,0.07 0.27,0.5,0.7 0.15,0.35,0.63 0,0,0.07 1,1,1 0,0,0
(C22) 0.09,0.3,0.5 0,0,0.05 0.01,0.09,0.25 0.05,0.21,0.45 0.01,0.09,0.25 1,1,1 0,0,0
(C23) 0,0.05,0.21 0,0.1,0.3 0,0,0.03 0,0,0.03 0,0.05,0.21 1,1,1 0,0,0
(C31) 0,0,0.07 0.03,0.15,0.35 0.27,0.5,0.7 0.27,0.5,0.7 0,0,0.07 1,1,1 0,0,0
(C32) 0,0.1,0.3 0,0,0.03 0,0.1,0.3 0,0.1,0.3 0,0.05,0.21 1,1,1 0,0,0
(C33) 0.09,0.3,0.5 0.03,0.15,0.35 0.09,0.3,0.5 0.03,0.15,0.35 0,0,0.05 1,1,1 0,0,0
(C34) 0,0,0.03 0,0.03,0.15 0,0.1,0.3 0,0,0.03 0,0.07,0.27 1,1,1 0,0,0
(C41) 0.01,0.09,0.25 0.01,0.09,0.25 0.09,0.3,0.5 0,0,0.05 0.03,0.15,0.35 1,1,1 0,0,0
(C42) 0,0.1,0.3 0,0,0.03 0,0.07,0.27 0,0.03,0.15 0,0.07,0.27 1,1,1 0,0,0
(C43) 0.05,0.21,0.45 0.09,0.3,0.5 0.01,0.09,0.25 0,0,0.05 0.01,0.09,0.25 1,1,1 0,0,0
(C44) 0,0.1,0.3 0,0.05,0.21 0,0.07,0.27 0,0.05,0.21 0,0,0.03 1,1,1 0,0,0
(C51) 0.09,0.3,0.5 0.03,0.15,0.35 0.03,0.15,0.35 0.09,0.3,0.5 0,0,0.05 1,1,1 0,0,0
(C52) 0.45,0.7,0.9 0.45,0.7,0.9 0.05,0.21,0.45 0,0,0.09 0,0,0.09 1,1,1 0,0,0
(C53) 0,0,0.03 (0,0,0.03) 0,0.1,0.3 0,0.05,0.21 0,0.05,0.21 1,1,1 0,0,0
di+ 13.6642 13.2785 13.7867 15.0051 15.3456
diˉ 4.1507 4.0976 4.1228 2.61662 2.4222
CCi 0.2330 0.2358 0.2302 0.1485 0.1363
Table 13: The order of ranking of the alternatives for different methods
Preference Order 1 2 3 4 5
TOPSIS WA2 WA3 WA4 WA1 WA5
Fuzzy TOPSIS WA2 WA1 WA3 WA4 WA5
The aim of the proposed methodology is to recommend a systematic evaluation model to improve the TWSQ including the comparison of both TOPSIS and Fuzzy TOPSIS, to find out the effective travel agency websites. The proposed methodology provides a systematic approach to narrow down the number of alternatives and to
all aspects, such as strategy, marketing, and technology to evaluate TWSQ.
5.
CONCLUSIONS
As a result of the rapid development of information and communication technologies, customers have gained access to a wide range of new services on the Internet. To help travel service providers better understand how the online customers view their services relative to their competitors, a customer-driven model of TWSQ is a crucial management for the travel managers. Through establishing a proper and effective evaluation model for assessing the TWSQ, it can identify criteria and find the relative importance of criteria. The proposed models can provide a guideline for the travel managers to provide appropriate levels of service quality in response to
customers’ needs.
The present study explored the use of TOPSIS and fuzzy TOPSIS in solving a TWSQ problem. The aim was to investigate the dimensions of
online travel service quality, by adapting and extending the TOPSIS and fuzzy TOPSIS models. Moreover, the methods and experiences learned from the study can be valuable to the company’s future strategic planning. Empirical results showed that the proposed methods are viable approaches in solving the proposed TWSQ problem. TOPSIS is a viable method for the proposed problem and is suitable for the use of precise performance ratings. When the performance ratings are vague and inaccurate, then the fuzzy TOPSIS is the preferred technique. In addition, there exists other worth investigating MADM methods for a travel website service quality problem. This becomes one of the future research opportunities in this classical yet important research area.
Sampling is a major limitation in this study. Since the survey was conducted based on a sample in Bangladesh, the prudent reader may need to interpret the results of the study with caution, particularly with respect to the generalization of research findings to Bangladesh travel service providers as a whole.
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